Classical Statistical Entropy of Black Hole

Dipo Mahto; Ved Prakash; Krishna Murari Singh; Brajnandan Kumar

doi:doi:10.11648/j.ajtas.s.2015040101.13

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Classical Statistical Entropy of Black Hole

Dipo Mahto, Ved Prakash, Krishna Murari Singh, Brajnandan Kumar

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 1-1)

Received: 2 July 2014 Accepted: 30 December 2014 Published: 5 February 2015

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Abstract

The present article derives an expression for classical statistical entropy of black hole using Maxwell- Boltzmann statistics and shows that the classical statistical entropy is directly proportional to the area of event horizon of black hole leading the result as SbhαA(r). No primary and secondary data is used in this paper. We have designed the work similar to the work of Ren Zhao and Shuang-Qi Hu who obtained the quantum statistical entropy corresponding to the black hole horizon using Femi-Dirac & Bose-Einstein statistics. They have also shown that the entropy corresponding to the black hole horizon surface is the entropy of quantum state near the surface of the horizon. It is completely theoretical based work using Laptop done at Marwari College research laboratory and the residential research chamber of first author.

Published in	American Journal of Theoretical and Applied Statistics (Volume 4, Issue 1-1) This article belongs to the Special Issue Computational Statistics
DOI	10.11648/j.ajtas.s.2015040101.13
Page(s)	15-18
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Statistical Entropy, Event Horizon, Black Hole

References

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[2]	Alfred,H.www.scribd.com/doc/22056940/statisticalmechanics(2009).
[3]	Cohen, E. G. D. "Boltzmann and Einstein: Statistics and dynamics—An unsolved problem." Pramana 64.5 (2005): 635-643.‏
[4]	Zhao R., Zhang Z. and Zhang S. “Uncertainty relation and black hole entropy of NUT-Kerr Newmann space-time.” Commun. Theoretical Physics (Beijing, China), Doi 10.393/ncb/i2004-10191-9, Vol.120B.1(2005):61-67.
[5]	Zhao R., Zhang J. and Zhang L. “Statistical entropy of axial symmetry Einstein-Maxwell-Dilation axion black holes.” Bulgarian Journal of Physics 28.5/6(2001) :200-208.
[6]	Hawking S. W. “Particle creation by black hole.” Communication in Mathematical Physics. 43(1975):199-220.
[7]	Bekenstein J. D. “Black holes and Entropy.” Phys. Rev. D 7, (1973):2333-2346.
[8]	G. W. Gibbons and S. W. Hawking: Cosmological event horizons, thermodynamics and particle creation, Phys. Rev. D 15, (1977): 2738.
[9]	Hooft G.’t “On quantum structure of a black hole.” Nucl. Phys. B256, (1985):727-745.
[10]	Zhao R. and Shuang-Qi H. “Quantum Statistical Entropy of the 5-Dimensional Stringy Black Hole.” Chinese Journal of Physics, 44.3(2006):172-179.
[11]	Zhao R., Wu Y. and Zhang S.(2006): “Quantum Statistical Entropy of Five-Dimensional Black Hole.” Commun. Theoretical Physics(Beijing, China) 45.5(2006):849–852.
[12]	Zhao R., Zhang L., Wu Y., and Li H.(2008): “Entropy of Four-Dimensional Spherically Symmetric Black Holes with Planck Length.” Commun. Theoretical Physics (Beijing, China) 50.6(2008):1327–1330.
[13]	Strominger, A. “Black hole entropy from near horizon microstates.” J. High Energy Phys. 02(1998):1-10.
[14]	Hawking, S. “A Brief History of Time.” Bantam Books, New York. ISBN:0-553-38016-8(1998).
[15]	Transchen, J. “An introduction to black hole evaporation.” arXiv: gr-qc/0010055V1(2000):1-32.
[16]	Wald, R.M. “The thermodynamics of black hole.” Living Reviews in Relativity ,4(2001):1-42.

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APA Style

Dipo Mahto, Ved Prakash, Krishna Murari Singh, Brajnandan Kumar. (2015). Classical Statistical Entropy of Black Hole. American Journal of Theoretical and Applied Statistics, 4(1-1), 15-18. https://doi.org/10.11648/j.ajtas.s.2015040101.13

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ACS Style

Dipo Mahto; Ved Prakash; Krishna Murari Singh; Brajnandan Kumar. Classical Statistical Entropy of Black Hole. Am. J. Theor. Appl. Stat. 2015, 4(1-1), 15-18. doi: 10.11648/j.ajtas.s.2015040101.13

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AMA Style

Dipo Mahto, Ved Prakash, Krishna Murari Singh, Brajnandan Kumar. Classical Statistical Entropy of Black Hole. Am J Theor Appl Stat. 2015;4(1-1):15-18. doi: 10.11648/j.ajtas.s.2015040101.13

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@article{10.11648/j.ajtas.s.2015040101.13,
  author = {Dipo Mahto and Ved Prakash and Krishna Murari Singh and Brajnandan Kumar},
  title = {Classical Statistical Entropy of Black Hole},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {1-1},
  pages = {15-18},
  doi = {10.11648/j.ajtas.s.2015040101.13},
  url = {https://doi.org/10.11648/j.ajtas.s.2015040101.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2015040101.13},
  abstract = {The present article derives an expression for classical statistical entropy of black hole using Maxwell- Boltzmann statistics and shows that the classical statistical entropy is directly proportional to the area of event horizon of black hole leading the result as SbhαA(r). No primary and secondary data is used in this paper. We have designed the work similar to the work of Ren Zhao and Shuang-Qi Hu who obtained the quantum statistical entropy corresponding to the black hole horizon using Femi-Dirac & Bose-Einstein statistics. They have also shown that the entropy corresponding to the black hole horizon surface is the entropy of quantum state near the surface of the horizon. It is completely theoretical based work using Laptop done at Marwari College research laboratory and the residential research chamber of first author.},
 year = {2015}
}

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TY  - JOUR
T1  - Classical Statistical Entropy of Black Hole
AU  - Dipo Mahto
AU  - Ved Prakash
AU  - Krishna Murari Singh
AU  - Brajnandan Kumar
Y1  - 2015/02/05
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.s.2015040101.13
DO  - 10.11648/j.ajtas.s.2015040101.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 15
EP  - 18
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.s.2015040101.13
AB  - The present article derives an expression for classical statistical entropy of black hole using Maxwell- Boltzmann statistics and shows that the classical statistical entropy is directly proportional to the area of event horizon of black hole leading the result as SbhαA(r). No primary and secondary data is used in this paper. We have designed the work similar to the work of Ren Zhao and Shuang-Qi Hu who obtained the quantum statistical entropy corresponding to the black hole horizon using Femi-Dirac & Bose-Einstein statistics. They have also shown that the entropy corresponding to the black hole horizon surface is the entropy of quantum state near the surface of the horizon. It is completely theoretical based work using Laptop done at Marwari College research laboratory and the residential research chamber of first author.
VL  - 4
IS  - 1-1
ER  -

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Author Information

Dipo Mahto

Department of Physics, Marwari College, T. M. B. U. Bhagalpur, Bhagalpur, India
Ved Prakash

University Department of Statistics & Computer Application, T. M. B. U. Bhagalpur, Bhagalpur, India
Krishna Murari Singh

Department of Physics, Marwari College, T. M. B. U. Bhagalpur, Bhagalpur, India
Brajnandan Kumar

University Department of Statistics & Computer Application, T. M. B. U. Bhagalpur, Bhagalpur, India

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APA Style

Dipo Mahto, Ved Prakash, Krishna Murari Singh, Brajnandan Kumar. (2015). Classical Statistical Entropy of Black Hole. American Journal of Theoretical and Applied Statistics, 4(1-1), 15-18. https://doi.org/10.11648/j.ajtas.s.2015040101.13

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ACS Style

Dipo Mahto; Ved Prakash; Krishna Murari Singh; Brajnandan Kumar. Classical Statistical Entropy of Black Hole. Am. J. Theor. Appl. Stat. 2015, 4(1-1), 15-18. doi: 10.11648/j.ajtas.s.2015040101.13

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AMA Style

Dipo Mahto, Ved Prakash, Krishna Murari Singh, Brajnandan Kumar. Classical Statistical Entropy of Black Hole. Am J Theor Appl Stat. 2015;4(1-1):15-18. doi: 10.11648/j.ajtas.s.2015040101.13

Copy | Download

@article{10.11648/j.ajtas.s.2015040101.13,
  author = {Dipo Mahto and Ved Prakash and Krishna Murari Singh and Brajnandan Kumar},
  title = {Classical Statistical Entropy of Black Hole},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {1-1},
  pages = {15-18},
  doi = {10.11648/j.ajtas.s.2015040101.13},
  url = {https://doi.org/10.11648/j.ajtas.s.2015040101.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2015040101.13},
  abstract = {The present article derives an expression for classical statistical entropy of black hole using Maxwell- Boltzmann statistics and shows that the classical statistical entropy is directly proportional to the area of event horizon of black hole leading the result as SbhαA(r). No primary and secondary data is used in this paper. We have designed the work similar to the work of Ren Zhao and Shuang-Qi Hu who obtained the quantum statistical entropy corresponding to the black hole horizon using Femi-Dirac & Bose-Einstein statistics. They have also shown that the entropy corresponding to the black hole horizon surface is the entropy of quantum state near the surface of the horizon. It is completely theoretical based work using Laptop done at Marwari College research laboratory and the residential research chamber of first author.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Classical Statistical Entropy of Black Hole
AU  - Dipo Mahto
AU  - Ved Prakash
AU  - Krishna Murari Singh
AU  - Brajnandan Kumar
Y1  - 2015/02/05
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.s.2015040101.13
DO  - 10.11648/j.ajtas.s.2015040101.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 15
EP  - 18
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.s.2015040101.13
AB  - The present article derives an expression for classical statistical entropy of black hole using Maxwell- Boltzmann statistics and shows that the classical statistical entropy is directly proportional to the area of event horizon of black hole leading the result as SbhαA(r). No primary and secondary data is used in this paper. We have designed the work similar to the work of Ren Zhao and Shuang-Qi Hu who obtained the quantum statistical entropy corresponding to the black hole horizon using Femi-Dirac & Bose-Einstein statistics. They have also shown that the entropy corresponding to the black hole horizon surface is the entropy of quantum state near the surface of the horizon. It is completely theoretical based work using Laptop done at Marwari College research laboratory and the residential research chamber of first author.
VL  - 4
IS  - 1-1
ER  -

Copy | Download